We give some new characterizations for compactness of weighted
composition operators $uC_\varphi$ acting on Bloch-type spaces in
terms of the power of the components of $\varphi,$ where $\varphi$
is a holomorphic self-map of the polydisk $\mathbb{D}^n,$ thus
generalizing the results obtained by HyvÃ¤rinen and
LindstrÃ¶m in 2012.

In this paper we give a description of separating or disjointness preserving linear bijections on spaces of vector-valued absolutely continuous functions defined on compact subsets of the real line. We obtain that they are continuous and biseparating in the finite-dimensional case. The infinite-dimensional case is also studied.